The common paradigm for quantum chemical descriptions of
strongly correlated systems of electrons is to decompose the overall correlation into static and dynamic components. The former
originates from a set of strongly coupled configurations whereas the latter stems from the remaining, weakly coupled ones.
Transition metal complexes with multiple unpaired electrons and bond formation/cleavage are typical examples of strongly correlated systems.
Yet, it is hardly possible to select manually the full set of strongly coupled many-electron configurations,
apart from a few of them that can be guessed by virtue of chemical or physical intuitions. One way out is to preselect a small number (\(n_o\) ) of frontier Hartree-Fock (HF) or
restricted open-shell Hartree-Fock (ROHF) orbitals and then allow
\(n_e\)  electrons to occupy such active orbitals in all possible ways, thereby leading to a complete active space (CAS) that is usually denoted as CAS\((n_e, n_o\) ).
If the space is directly diagonalized to account for interactions between the configurations, one would have a simple CASCI approach, with CI standing for configuration interaction.
However, it is often the case that HF/ROHF orbitals are very poor for correlation, such that it is necessary to reoptimize them along with the CI coefficients or simply replace them
with other type of orbitals (e.g., natural orbitals (NO) generated in one way or another[1]}, [2]}, [3]}, [4]}).
The former leads to the so-called CASSCF method[5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, which has
long been the cornerstone of ab initio quantum chemistry for strong correlation thanks to its operational simplicity
as well as ever improved algorithms[12]}, [13]}, [14]}. Nevertheless, CASSCF
has been plagued by several factors: (1) it is by no means trivial to select which and how many orbitals as active orbitals. (2) It is often the case
that some desired active orbitals run out of the CAS during the self-consistent field (SCF) iterations, thereby resulting in undesired solutions or
no convergence. (3) It is
particularly difficult to maintain the same CAS when scanning potential energy surfaces. (4) The size of CAS grows combinatorially with respect to \(n_o\)  and \(n_e\) ,
to name just the major ones. While the combinatorial complexity can be alleviated to a large extent by imposing certain restrictions on the occupation patterns so as to a priori reduce
the space size[15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]} or by using some highly efficient posteriori selection schemes as the CI solver[28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}, [36]}, [37]}, [38]}, [39]}, [40]}, [41]}, [42]}, [43]}, [44]},
the first three issues pertinent to orbital selection and optimization are more delicate. Although the selection of active orbitals can be automated by
using, e.g, occupation numbers of NOs[1]}, [2]}, [3]}, [4]}, [49]}, [50]}, information entropies[51]}, [52]}, [53]},
machine learning[54]}, subspace projection[55]}, [56]}, [57]}, stepwise testing[58]}, etc., the so-constructed CAS
cannot be guaranteed to be the same for all geometries of complex systems due to the underlying cutoff thresholds or varying parameters.
Herewith, we propose an automated approach for constructing a CAS that is guaranteed to be the same for all geometries. Like the subspace projection approaches[55]}, [56]},
it is based on the (minimal) assumption that the electronic states of interest have largest projections onto a prechosen subspace. However, our approach originates actually from the generic idea of “from fragments to molecule” (F2M) for constructing localized molecular orbitals (LMO)[61]}, [62]}, [63]}, [64]},
by regarding atoms also as fragments. A set of pre-LMOs can readily be constructed from the prechosen atomic/fragmental orbitals
and are then used as probes to
select automatically initial local active orbitals. The CASSCF orbitals can also be localized in each iteration so as to facilitate the matching of
orbitals between two adjacent iterations. Since the selection of both initial and optimized local active orbitals is imposed from the very beginning
by the pre-LMOs (which span the same space as the prechosen atomic/fragmental orbitals), this approach will be dubbed as “imposed CASSCF” (\(\mathbb {i}\) CASSCF or simply \(\mathbb {i}\) CAS in short).
It should not be confused with the iCASSCF approach[41]} that solves the CAS problem in terms of increments.
The algorithms are described in detail in Sec. . The efficacy of \(\mathbb {i}\) CAS
will be revealed in Sec.  by taking both organic molecules and transition metal complexes as examples.
The presentation is closed with concluding remarks Sec. .
